primitive
¶
Module dedicated for basic primitive.

Convex hulls in N dimensions. 

Return angles for Cartesian 3D coordinates x, y, and z. 

Return homogeneous rotation matrix from Euler angles and axis sequence. 

Triangulate a set of vertices on the sphere. 

Return corrected triangles. 

Join two or more pathname components, inserting ‘/’ as needed. 

Return vertices and triangle for a box geometry. 
Return vertices and triangles for icosahedron. 


Provide vertices and triangles of the spheres. 
Return vertices and triangles for a square geometry. 


Provide vertices and triangles of a superquadrics. 
Return vertices and triangles for a tetrahedron. 


Repeat Vertices and triangles of a specific primitive shape. 

Repeat Vertices and triangles of a specific primitive function. 
ConvexHull
¶

class
fury.primitive.
ConvexHull
(points, incremental=False, qhull_options=None)¶ Bases:
scipy.spatial.qhull._QhullUser
Convex hulls in N dimensions.
New in version 0.12.0.
 Parameters
points (ndarray of floats, shape (npoints, ndim)) – Coordinates of points to construct a convex hull from
incremental (bool, optional) – Allow adding new points incrementally. This takes up some additional resources.
qhull_options (str, optional) – Additional options to pass to Qhull. See Qhull manual for details. (Default: “Qx” for ndim > 4 and “” otherwise) Option “Qt” is always enabled.

points
¶ Coordinates of input points.
 Type
ndarray of double, shape (npoints, ndim)

vertices
¶ Indices of points forming the vertices of the convex hull. For 2D convex hulls, the vertices are in counterclockwise order. For other dimensions, they are in input order.
 Type
ndarray of ints, shape (nvertices,)

simplices
¶ Indices of points forming the simplical facets of the convex hull.
 Type
ndarray of ints, shape (nfacet, ndim)

neighbors
¶ Indices of neighbor facets for each facet. The kth neighbor is opposite to the kth vertex. 1 denotes no neighbor.
 Type
ndarray of ints, shape (nfacet, ndim)

equations
¶ [normal, offset] forming the hyperplane equation of the facet (see Qhull documentation for more).
 Type
ndarray of double, shape (nfacet, ndim+1)

coplanar
¶ Indices of coplanar points and the corresponding indices of the nearest facets and nearest vertex indices. Coplanar points are input points which were not included in the triangulation due to numerical precision issues.
If option “Qc” is not specified, this list is not computed.
 Type
ndarray of int, shape (ncoplanar, 3)

good
¶ A onedimensional Boolean array indicating which facets are good. Used with options that compute good facets, e.g. QGn and QGn. Good facets are defined as those that are visible (n) or invisible (n) from point n, where n is the nth point in ‘points’. The ‘good’ attribute may be used as an index into ‘simplices’ to return the good (visible) facets: simplices[good]. A facet is visible from the outside of the hull only, and neither coplanarity nor degeneracy count as cases of visibility.
If a “QGn” or “QGn” option is not specified, None is returned.
New in version 1.3.0.
 Type
ndarray of bool or None
 Raises
QhullError – Raised when Qhull encounters an error condition, such as geometrical degeneracy when options to resolve are not enabled.
ValueError – Raised if an incompatible array is given as input.
Notes
The convex hull is computed using the Qhull library.
Examples
Convex hull of a random set of points:
>>> from scipy.spatial import ConvexHull, convex_hull_plot_2d >>> points = np.random.rand(30, 2) # 30 random points in 2D >>> hull = ConvexHull(points)
Plot it:
>>> import matplotlib.pyplot as plt >>> plt.plot(points[:,0], points[:,1], 'o') >>> for simplex in hull.simplices: ... plt.plot(points[simplex, 0], points[simplex, 1], 'k')
We could also have directly used the vertices of the hull, which for 2D are guaranteed to be in counterclockwise order:
>>> plt.plot(points[hull.vertices,0], points[hull.vertices,1], 'r', lw=2) >>> plt.plot(points[hull.vertices[0],0], points[hull.vertices[0],1], 'ro') >>> plt.show()
Facets visible from a point:
Create a square and add a point above the square.
>>> generators = np.array([[0.2, 0.2], ... [0.2, 0.4], ... [0.4, 0.4], ... [0.4, 0.2], ... [0.3, 0.6]])
Call ConvexHull with the QG option. QG4 means compute the portions of the hull not including point 4, indicating the facets that are visible from point 4.
>>> hull = ConvexHull(points=generators, ... qhull_options='QG4')
The “good” array indicates which facets are visible from point 4.
>>> print(hull.simplices) [[1 0] [1 2] [3 0] [3 2]] >>> print(hull.good) [False True False False]
Now plot it, highlighting the visible facets.
>>> fig = plt.figure() >>> ax = fig.add_subplot(1,1,1) >>> for visible_facet in hull.simplices[hull.good]: ... ax.plot(hull.points[visible_facet, 0], ... hull.points[visible_facet, 1], ... color='violet', ... lw=6) >>> convex_hull_plot_2d(hull, ax=ax) <Figure size 640x480 with 1 Axes> # may vary >>> plt.show()
References
 Qhull

__init__
()¶

add_points
¶ Process a set of additional new points.
 Parameters
points (ndarray) – New points to add. The dimensionality should match that of the initial points.
restart (bool, optional) – Whether to restart processing from scratch, rather than adding points incrementally.
 Raises
QhullError – Raised when Qhull encounters an error condition, such as geometrical degeneracy when options to resolve are not enabled.
See also
close
Notes
You need to specify
incremental=True
when constructing the object to be able to add points incrementally. Incremental addition of points is also not possible after close has been called.

property
points

property
vertices
cart2sphere¶

fury.primitive.
cart2sphere
(x, y, z)[source]¶ Return angles for Cartesian 3D coordinates x, y, and z.
See doc for
sphere2cart
for angle conventions and derivation of the formulae.$0lethetamathrm{(theta)}lepi$ and $pilephimathrm{(phi)}lepi$
 Parameters
x (array_like) – x coordinate in Cartesian space
y (array_like) – y coordinate in Cartesian space
z (array_like) – z coordinate
 Returns
r (array) – radius
theta (array) – inclination (polar) angle
phi (array) – azimuth angle
euler_matrix¶

fury.primitive.
euler_matrix
(ai, aj, ak, axes='sxyz')[source]¶ Return homogeneous rotation matrix from Euler angles and axis sequence.
Code modified from the work of Christoph Gohlke link provided here http://www.lfd.uci.edu/~gohlke/code/transformations.py.html
 Parameters
aj, ak (ai,) –
axes (One of 24 axis sequences as string or encoded tuple) –
 Returns
matrix (ndarray (4, 4))
Code modified from the work of Christoph Gohlke link provided here
http (//www.lfd.uci.edu/~gohlke/code/transformations.py.html)
Examples
>>> import numpy >>> R = euler_matrix(1, 2, 3, 'syxz') >>> numpy.allclose(numpy.sum(R[0]), 1.34786452) True >>> R = euler_matrix(1, 2, 3, (0, 1, 0, 1)) >>> numpy.allclose(numpy.sum(R[0]), 0.383436184) True >>> ai, aj, ak = (4.0*math.pi) * (numpy.random.random(3)  0.5) >>> for axes in _AXES2TUPLE.keys(): ... _ = euler_matrix(ai, aj, ak, axes) >>> for axes in _TUPLE2AXES.keys(): ... _ = euler_matrix(ai, aj, ak, axes)
faces_from_sphere_vertices¶
fix_winding_order¶

fury.primitive.
fix_winding_order
(vertices, triangles, clockwise=False)[source]¶ Return corrected triangles.
Given an ordering of the triangle’s three vertices, a triangle can appear to have a clockwise winding or counterclockwise winding. Clockwise means that the three vertices, in order, rotate clockwise around the triangle’s center.
 Parameters
vertices (ndarray) – array of vertices corresponding to a shape
triangles (ndarray) – array of triangles corresponding to a shape
clockwise (bool) – triangle order type: clockwise (default) or counterclockwise.
 Returns
corrected_triangles – The corrected order of the vert parameter
 Return type
ndarray
pjoin¶

fury.primitive.
pjoin
(a, *p)¶ Join two or more pathname components, inserting ‘/’ as needed. If any component is an absolute path, all previous path components will be discarded. An empty last part will result in a path that ends with a separator.
prim_box¶
prim_icosahedron¶
prim_sphere¶

fury.primitive.
prim_sphere
(name='symmetric362', gen_faces=False)[source]¶ Provide vertices and triangles of the spheres.
 Parameters
name (str) – which sphere  one of: * ‘symmetric362’ * ‘symmetric642’ * ‘symmetric724’ * ‘repulsion724’ * ‘repulsion100’ * ‘repulsion200’
gen_faces (bool, optional) – If True, triangulate a set of vertices on the sphere to get the faces. Otherwise, we load the saved faces from a file. Default: False
 Returns
vertices (ndarray) – vertices coords that composed our sphere
triangles (ndarray) – triangles that composed our sphere
Examples
>>> import numpy as np >>> from fury.primitive import prim_sphere >>> verts, faces = prim_sphere('symmetric362') >>> verts.shape == (362, 3) True >>> faces.shape == (720, 3) True
prim_square¶
prim_superquadric¶

fury.primitive.
prim_superquadric
(roundness=(1, 1), sphere_name='symmetric362')[source]¶ Provide vertices and triangles of a superquadrics.
 Parameters
 Returns
vertices (ndarray) – vertices coords that composed our sphere
triangles (ndarray) – triangles that composed our sphere
Examples
>>> import numpy as np >>> from fury.primitive import prim_superquadric >>> verts, faces = prim_superquadric(roundness=(1, 1)) >>> verts.shape == (362, 3) True >>> faces.shape == (720, 3) True
prim_tetrahedron¶
repeat_primitive¶

fury.primitive.
repeat_primitive
(vertices, faces, centers, directions=(1, 0, 0), colors=(255, 0, 0), scale=1, have_tiled_verts=False)[source]¶ Repeat Vertices and triangles of a specific primitive shape.
It could be seen as a glyph.
 Parameters
vertices (ndarray) – vertices coords to duplicate at the centers positions
triangles (ndarray) – triangles that composed our shape to duplicate
centers (ndarray, shape (N, 3)) – Superquadrics positions
directions (ndarray, shape (N, 3) or tuple (3,), optional) – The orientation vector of the cone.
colors (ndarray (N,3) or (N, 4) or tuple (3,) or tuple (4,)) – RGB or RGBA (for opacity) R, G, B and A should be at the range [0, 1]
scale (ndarray, shape (N) or (N,3) or float or int, optional) – The height of the cone.
have_tiled_verts (bool) – option to control if we need to duplicate vertices of a shape or not
 Returns
big_vertices (ndarray) – Expanded vertices at the centers positions
big_triangles (ndarray) – Expanded triangles that composed our shape to duplicate
big_colors (ndarray) – Expanded colors applied to all vertices/faces
big_centers (ndarray) – Expanded centers for all vertices/faces
repeat_primitive_function¶

fury.primitive.
repeat_primitive_function
(func, centers, func_args=[], directions=(1, 0, 0), colors=(255, 0, 0), scale=1)[source]¶ Repeat Vertices and triangles of a specific primitive function.
It could be seen as a glyph. The primitive function should generate and return vertices and faces
 Parameters
func (callable) – primitive functions
centers (ndarray, shape (N, 3)) – Superquadrics positions
func_args (args) – primitive functions arguments/parameters
directions (ndarray, shape (N, 3) or tuple (3,), optional) – The orientation vector of the cone.
colors (ndarray (N,3) or (N, 4) or tuple (3,) or tuple (4,)) – RGB or RGBA (for opacity) R, G, B and A should be at the range [0, 1]
scale (ndarray, shape (N) or (N,3) or float or int, optional) – The height of the cone.
 Returns
big_vertices (ndarray) – Expanded vertices at the centers positions
big_triangles (ndarray) – Expanded triangles that composed our shape to duplicate
big_colors (ndarray) – Expanded colors applied to all vertices/faces